There are several woolen mills still operating in Ireland, spinning Irish (and foreign yarns):
Donegal Woollen Mills
This mill produces mainly tweed yarns and is possibly best known for its Kilcarra Aran Tweed which has recently been renamed to Studio Donegal.
Here is a great blog post about a visit to the Donegal Mill.
Cushendale Woollen Mills
Cushendale produce yarn & fabrics. Some of the yarns they produce include 4 ply & DK 100% wool and 70% Mohair 30% Wool Bouclé.
I recently visited Cushendale Mills in Graignamanagh, Co. Kilkenny and I blogged about it here.
Kerry Woollen Mills
This mill produces carded wool for spinning as well as aran and aran tweed yarn.
You can read a short blog post about it here.
If anyone has blogged about a visit here, please contact me & let me know & I'll link to your post here.